iMechanica - Comments for "a question about vibration of plates having variable thickness "
https://imechanica.org/node/12791
Comments for "a question about vibration of plates having variable thickness "enWhy you don't use
https://imechanica.org/comment/19344#comment-19344
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<p><em>In reply to <a href="https://imechanica.org/node/12791">a question about vibration of plates having variable thickness </a></em></p>
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Why you don't use a combination of Sin(m.Pi.x).Sin(n.Pi.y) which is a logical Choice in Vibration Analysis. Don't neglect the effect of Symmetric, Anti-symmetric modes,.....in all directions.
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Your analysis is similar to Weighted Residuals which are Approximation Methods. In this case you need to Know the Differential Equation of Motion of your Plate, Choose the Trial (or approximation) Function and then Minimize the Integral of the Weighted Residual in the Analysed Domain. The Solution may Converge to the Exact in some Applications. It Depends on the Important Choice of the Trial Function.
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mohammed lamine Moussaoui
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</ul>Wed, 18 Jul 2012 10:18:42 +0000mohammedlaminecomment 19344 at https://imechanica.orgUnfortunately, my knowledge
https://imechanica.org/comment/19338#comment-19338
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<p><em>In reply to <a href="https://imechanica.org/comment/19337#comment-19337">Re: Vibration of Plates having Variable Thickness</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Unfortunately, my knowledge on FEM is very shallow. functions we use to approximate the function w(x,y) must satisfy boundary conditions. therefore we choose for example sin(Pi.x) for simply-supported boundary conditions along x-axis. It is seems these approaches (FEM & semi-analytical) are a little different. I found two old papers "Forced vibrations of a non-uniform thickness rectangular plate with two free sides 1979" and "A semi-analytic solution for free vibration of rectangular plates 1978" in which w(x,y)=f(y)sin(Pi.x) for plates with variable thicknesses. It seems we can use this approach based on these two papers. many thanks Mohammed</p>
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</ul>Mon, 16 Jul 2012 20:31:34 +0000sayad.boreyricomment 19338 at https://imechanica.orgRe: Vibration of Plates having Variable Thickness
https://imechanica.org/comment/19337#comment-19337
<a id="comment-19337"></a>
<p><em>In reply to <a href="https://imechanica.org/node/12791">a question about vibration of plates having variable thickness </a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi boreyri,
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In Finite Elements the Displacement w(x,y) is chosen as a Polynomial function by using Pascal's Triangle.
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Thus in your case we can use the Interpolation functions to define
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the variation of your Linearly (or other variation) Variable Thickness before calculating the
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Stiffness Matrix of the Plate Bending Element.
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Is your approximation similar to this analysis ?
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Sincerely
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Mohammed lamine
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</ul>Mon, 16 Jul 2012 20:06:46 +0000mohammedlaminecomment 19337 at https://imechanica.org